Chaotic spatial bifurcation by complex coupling.

A spatial bifurcation (a transition from stationary to oscillatory regime) in a chain of unidirectionally coupled phase systems is studied. It is shown that complication of coupling terms can make this bifurcation spatially chaotic in contrast to the previously observed "regular" and "predictable" type. It is demonstrated that the found type of spatial bifurcation corresponds to a smooth (predictable) manifold in the parameter space, while its spatial location gets actually unpredictable being governed by regularities of chaotic behavior.

Network mechanism for burst generation.

We report on the mechanism of burst generation by populations of intrinsically spiking neurons, when a certain threshold in coupling strength is exceeded. These ensembles synchronize at relatively low coupling strength and lose synchronization at stronger coupling via spatiotemporal intermittency. The latter transition triggers fast repetitive spiking, which results in synchronized bursting.

Phase synchronization in ensembles of bursting oscillators.

We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously.

Phase synchronization of chaotic intermittent oscillations.

We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.